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Characterizing and extending answer set semantics using possibility theory

KIM BAUTERS, STEVEN SCHOCKAERT, MARTINE DE COCK, DIRK VERMEIR
2014 Theory and Practice of Logic Programming  
Special models of these constraints are then identified as possibilistic answer sets.  ...  In this paper we present new semantics for PASP in which rules are interpreted as constraints on possibility distributions.  ...  In addition, the new semantics allow us to uncover a new characterization of ASP in terms of possibility theory.  ... 
doi:10.1017/s147106841300063x fatcat:qi6sp2bwgveqzopi7ovxzagr7q

Page 7264 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
The paper develops a specific theory of the preferred answer sets semantics that is “situated” between (and succeeds in inte- grating extended) logic programs with preferred answer sets (G.  ...  characterized in a uniform way by their preferred answer sets.  ... 

Answer Set Programming and S4 [chapter]

Mauricio Osorio, Juan Antonio Navarro
2004 Lecture Notes in Computer Science  
As a consequence of our results we show how to present the well known semantics of answer sets, under a restricted fragment of modal formulas, using this approach.  ...  Our results clearly state interesting links between answer set programming, modal logics and multi-agent systems which might bring research of these areas together.  ...  Extending the syntax of logic formulas with new unary connectives and ♦, and giving an adequate semantical meaning to them, it is possible to define a formal system to model notions like knowledge, tense  ... 
doi:10.1007/978-3-540-30498-2_36 fatcat:nhebklhqrzdnjbfppy6jj6uz7q

Paraconsistent Stable Semantics for Extended Disjunctive Programs

CHIAKI SAKAMA, KATSUMI INOUE
1995 Journal of Logic and Computation  
These semantics are based on lattice-structured multi-valued logics, and are characterized by a new xpoint semantics of extended disjunctive programs.  ...  This paper presents declarative semantics of possibly inconsistent disjunctive logic programs.  ...  They extended Fitting's three-valued semantics of logic programming [11] and developed a theory for possibly inconsistent logic programs using Belnap's four-valued logic [4] .  ... 
doi:10.1093/logcom/5.3.265 fatcat:anlwztenxndnracmqpj6zx3tdy

Possibilistic Answer Set Programming Revisited [article]

Kim Bauters, Steven Schockaert, Martine De Cock, Dirk Vermeir
2012 arXiv   pre-print
Possibilistic answer set programming (PASP) extends answer set programming (ASP) by attaching to each rule a degree of certainty.  ...  To develop a more suitable semantics, we first introduce a characterization of answer sets of classical ASP programs in terms of possibilistic logic where an ASP program specifies a set of constraints  ...  Acknowledgements The authors would like to thank the anonymous reviewers for their useful comments, in particular for pointing out the link between our work and residuated logic programs.  ... 
arXiv:1203.3466v1 fatcat:djswyskstfbgrj6esaplg4erxm

Semantics of Horn and disjunctive logic programs

Jorge Lobo, Arcot Rajasekar, Jack Minker
1991 Theoretical Computer Science  
For this, we extend the fixpoint semantics and the operational or procedural semantics to the class of disjunctive logic programs and prove their equivalence using techniques similar to the ones used for  ...  Van Emden and Kowalski proposed a fixpoint semantics based on model-theory and an operational semantics based on proof-theory for Horn logic programs.  ...  Acknowledgment We wish to express our appreciation to the National Science Foundation for their support of our work under grant number IRI-86-09170 and the Army Research Office under grant number DAAG-  ... 
doi:10.1016/0304-3975(91)90006-n fatcat:caazixkcnfcrti5soh3jgiqsny

Negation as failure in the head

Katsumi Inoue, Chiaki Sakama
1998 The Journal of Logic Programming  
Through the simulation of negation as failure in the head, computation of answer sets and supported sets is realized using any proof procedure for extended or positive disjunctive programs.  ...  An interesting feature of such programs is that the minimality of answer sets does not hold.  ...  Acknowledgements Discussions with Alexander Bochman, Thomas Eiter, George Gottlob, Michael Gelfond, and Vladimir Lifschitz were helpful to make many ideas in this paper clear.  ... 
doi:10.1016/s0743-1066(97)10001-2 fatcat:pwhzjknxwjbzpoqmxfr3bvuxea

Question Meaning = Resolution Conditions

Ivano Ciardelli
2017 Logic and Logical Philosophy  
by answer-set theories.  ...  Traditional approaches to the semantics of questions analyze questions indirectly, via the notion of an answer.  ...  The ideas presented in this paper have benefited enormously from extensive discussions with Jeroen Groenendijk and Floris Roelofsen.  ... 
doi:10.12775/llp.2017.017 fatcat:fvabqtfwynbyjp3y53bxunhrwu

A General Framework for Equivalences in Answer-Set Programming by Countermodels in the Logic of Here-and-There [article]

Michael Fink
2010 arXiv   pre-print
In particular, uniform equivalence coincides under open and ordinary answer-set semantics, and for finite non-ground programs under these semantics, also the usual characterization of uniform equivalence  ...  We thus obtain a general framework for the study of various notions of equivalence for theories under answer-set semantics.  ...  This work was supported by the Austrian Science Fund (FWF) under grants P18019 and P20841, and by the Vienna Science and Technology Fund (WWTF) under project ICT08-020.  ... 
arXiv:1006.3021v1 fatcat:lgkgp5fmiba37ceekvuuwwq5r4

Disjunctive logic programming and autoepistemic logic [chapter]

Li -Yan Yuan, Jia -Huai You, Randy Goebel
1998 Lecture Notes in Computer Science  
In this paper, we use autoepistemic reasoning semantics to classify various semantics for disjunctive logic programs with default negation.  ...  We also observed that all logic program semantics fall into three semantical points of view: the skeptical, stable, and partial-stable.  ...  The answer set semantics is defined for extended logic programs that allow classical negation in both head and body while the stable circumscriptive semantics is defined for general autoepistemic theories  ... 
doi:10.1007/bfb0054791 fatcat:dmbwpa4grjegxlmgpffpvl2nmq

Hypothetical reasoning in logic programs

Katsumi Inoue
1994 The Journal of Logic Programming  
As an example of extended logic programs, Gelfond and Lifschitz [ll] consider the inference of negation using the closed world assumption, which can be represented by augmenting the program with rules  ...  The syntactical difference of our knowledge system-from Poole's framework is that, whereas the latter uses first-order logic, ours uses extended logic programs as a "host" language.  ...  The semantics of extended logic programs can be given in various ways: the answer set semantics [ll] , the extended stable semantics [33] , and others.  ... 
doi:10.1016/0743-1066(94)90043-4 fatcat:epm6iwmfurgpnmwuuhecfrz4am

Belief, provability, and logic programs

José Júlio Alferes, Luís Moniz Pereira
1995 Journal of Applied Non-Classical Logics  
Because of the newly established relationship between our epistemic logic and extended program semantics, the former benefits from the procedures and implementations of the latter, and can be applied to  ...  The main goal of this paper is to establish a nonmonotonic epistemic logic with two modalities -provability and belief -capable of expressing and comparing a variety of known semantics for extended logic  ...  Acknowledgments We acknowledge Esprit BRA Compulog 2 (no. 6810), and JNICT -Portugal for their support. Thanks to Carlos Damásio and Teodor Przymusinski for helpful discussions.  ... 
doi:10.1080/11663081.1995.10510842 fatcat:y2s4fqionjg6fnkbmysl7p5ixe

Semantics for Possibilistic Disjunctive Programs [article]

Juan Carlos Nieves, Mauricio Osorio, Ulises Cortés
2011 arXiv   pre-print
By considering a possibilistic logic program as a possibilistic logic theory, a construction of a possibilistic logic programming semantic based on answer sets and the proof theory of possibilistic logic  ...  It shows that this possibilistic semantics for disjunctive logic programs can be characterized by a fixed-point operator.  ...  in terms of the proof theory of possibilistic logic and the standard answer set semantics.  ... 
arXiv:1106.0776v1 fatcat:wgqq36wrtbcutib2s5ssnqtj6e

Safe beliefs for propositional theories

Mauricio Osorio, Juan Antonio Navarro Pérez, José Arrazola
2005 Annals of Pure and Applied Logic  
We propose an extension of answer sets, that we call safe beliefs, that can be used to study several properties and notions of answer sets and logic programming from a more general point of view.  ...  We also show that the answer set semantics satisfies an important property, the "extension by definition", that can be used to construct program translations.  ...  Acknowledgement Numerous discussions with David Pearce helped us to identify the relations between the safe beliefs approach and the equilibrium logic.  ... 
doi:10.1016/j.apal.2004.06.012 fatcat:v77hhsnxbrcujde3vgnnzhq54y

Getting unique solution in data exchange

Nhung Ngo, Enrico Franconi
2013 Proceedings of the VLDB Endowment  
We apply the framework to relational data exchange setting and solve the problem by pointing out minimal solutions according to a specific semantic minimality criterion.  ...  To make query answering feasible for all queries, we focus on a methodology for extending the original schema mapping to guarantee the uniqueness of target instance corresponding to a source instance.  ...  Tackle the problem in different data exchange settings by: • Finding solutions • Characterizing the language of extended schema mappings such that inexpensive and SQL-transformable ones are preferred •  ... 
doi:10.14778/2536274.2536332 fatcat:faqknfzjkvhgjngdh7y6xy67zy
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